A Σ-Δ modulator is widely implemented in connection with data conversion, e.g., the Σ-Δ modulator can be used in a digital-to-analog converter (DAC) or an analog-to-digital converter (ADC). The Σ-Δ modulator is classified as two types—a single-bit Σ-Δ modulator or a multi-bit Σ-Δ modulator. Since quantization noise of the multi-bit Σ-Δ modulator is much smaller than that of the single-bit Σ-Δ modulator, the multi-bit Σ-Δ modulator is more frequently employed. However, due to fabrication process differences between DACs or ADCs, mismatch noises or errors occur. In view of the foregoing description, a DEM mechanism is developed to reduce mismatch noises for noise-shaping. FIG. 1 shows a block diagram of a Σ-Δ modulator 10, a DEM 12 and a DAC 14. The DEM 12 comprises a plurality of controlled switches. The DEM 12 turns on or off the switches according to an output signal from the Σ-Δ modulator 10 so as to reduce mismatch noises.
In a conventional DEM mechanism, a dynamic weighting average (DWA) selectively turns on/off switches via a continuous alternative approach according to the number of to-be-turned-on switches. Table 1 illustrates an example of ten switches of which to-be-turned-on switches are marked by “V” and to-be-turned-off switches are not marked.
TABLE 1Number ofon/offMotionSwitches12345678910Activity3VVV—5VVVVV82VV78VVVVVVVV10 7VVVVVVV3
In this example, at the beginning, the first three switches are turned on. After that, a continuous series of five switches is turned on. The first switch is to be turned on until all of the ten switches are in sequence turned on once. A final item of Table 1 illustrates a switch activity representing the number of switches of which on/off statuses are changed when a previous signal traverses to a current signal. That is, the number of switches of which on/off statuses are changed is equal to the number of switches changing from being turned on to turned off adding to the number of switches changing from being turned off to turned on. For example, when a signal amplitude is large and is around a maximum point and a minimum point of a signal, the switch activity is small; when the signal amplitude is between the maximum point and the minimum point of the signal, the switch activity is large.
Although the foregoing conventional DWA technique is simple and is easily implemented, harmonic noise is created due to large switch activity when the conventional DWA technique is applied to a signal with large amplitude. The harmonic noises related with signal amplitude is also referred to as signal-related harmonic noises.
In view of the conventional DEM technique that cannot reduce mismatch noise, a novel DEM system and method thereof capable of maintaining DEM noise-shaping as well as reducing harmonic noise related with a signal with large amplitude is in need.